Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red,blue and green,then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps,is

If $5$ red roses and $5$ white roses of different sizes are used in preparing a garland,the probability that red and white roses come alternately is

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is:

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other is: